scholarly journals The algebraic construction of the Novikov complex of a circle-valued Morse function

2002 ◽  
Vol 322 (4) ◽  
pp. 745-785 ◽  
Author(s):  
Andrew Ranicki
Keyword(s):  
Morse Function ◽  
Algebraic Construction ◽  
Novikov Complex

Relations between Varshni and Morse potential energy parameters

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Teik-Cheng Lim ◽  
Rajendra Udyavara
Keyword(s):  
Potential Energy ◽  
Force Constant ◽  
Morse Potential ◽  
Morse Function ◽  
Energy Integral ◽  
Equal Energy ◽  
Molecular Force ◽  
Parameter Conversion ◽  
Bond Stretching ◽  
Small Change

AbstractA set of relationships between the Morse and Varshni potential functions for describing covalent bondstretching energy has been developed by imposing equal force constant and equal energy integral. In view of the extensive adoption of Morse function in molecular force fields, this paper suggests two sets of parameter conversions from Varshni to Morse. The parameter conversion based on equal force constant is applicable for small change in bond length, while the parameter conversion based on equal energy integral is more applicable for significant bond-stretching. Plotted results reveal that the Varshni potential function is more suitable for describing hard bonds rather than soft bonds.

scholarly journals An Algebraic Construction of a Class of One-Dependent Processes

1989 ◽  
Vol 17 (1) ◽  
pp. 128-143 ◽  
Author(s):  
Jon Aaronson ◽  
David Gilat ◽  
Michael Keane ◽  
Vincent de Valk
Keyword(s):  
Algebraic Construction ◽  
Dependent Processes

scholarly journals WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

2021 ◽  
pp. 1-38
Author(s):  
Xianzhe Dai ◽  
Junrong Yan
Keyword(s):  
Essential Role ◽  
Morse Function ◽  
Noncompact Manifold ◽  
Morse Inequalities ◽  
Bounded Geometry ◽  
Noncompact Manifolds ◽  
Witten Laplacian ◽  
Relative Cohomology ◽  
Witten Deformation ◽  
Small Eigenvalues

Abstract Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting.

Algebraic construction of a new class of quasi-orthogonal arrays for steganography

1999 ◽  
Author(s):  
Ron G. van Schyndel ◽  
Andrew Z. Tirkel ◽  
Imants D. Svalbe ◽  
Thomas E. Hall ◽  
Charles F. Osborne
Keyword(s):  
Orthogonal Arrays ◽  
Algebraic Construction ◽  
New Class

scholarly journals ALGEBRAIC ASPECT AND CONSTRUCTION OF LAX OPERATORS IN QUANTUM INTEGRABLE SYSTEMS

1995 ◽  
Vol 10 (40) ◽  
pp. 3113-3117 ◽  
Author(s):  
B. BASU-MALLICK ◽  
ANJAN KUNDU
Keyword(s):  
Integrable Systems ◽  
Integrable Models ◽  
Quantum Integrable Systems ◽  
Algebraic Construction ◽  
Algebraic Aspect ◽  
Quantum Integrable Models

An algebraic construction which is more general and closely connected with that of Faddeev,1 along with its application for generating different classes of quantum integrable models is summarized to complement the recent results of Ref. 1.

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